library(rstan)
library(survival)
library(tidyverse)
library(tidybayes)
# data, parameters, model and generated quantities blocks
Stan_exponential_survival_model <- "
data{
int <lower=1> N_uncensored;
int <lower=1> N_censored;
int <lower=0> numCovariates;
matrix[N_censored, numCovariates] X_censored;
matrix[N_uncensored, numCovariates] X_uncensored;
vector <lower=0>[N_censored] times_censored;
vector <lower=0>[N_uncensored] times_uncensored;
}
parameters{
vector[numCovariates] beta; //regression coefficients
real alpha; //intercept
}
model{
beta ~ normal(0,10); //prior on regression coefficients
alpha ~ normal(0,10); //prior on intercept
target += exponential_lpdf(times_uncensored | exp(alpha+X_uncensored * beta)); //log-likelihood part for uncensored times
target += exponential_lccdf(times_censored | exp(alpha+X_censored * beta)); //log-likelihood for censored times
}
generated quantities{
vector[N_uncensored] times_uncensored_sampled; //prediction of death
for(i in 1:N_uncensored) {
times_uncensored_sampled[i] = exponential_rng(exp(alpha+X_uncensored[i,]* beta));
}
}
"
# prepare the data
set.seed(42);
require (tidyverse);
data <- read_csv('../data.csv')
New names:
* `` -> ...1
Rows: 2066 Columns: 12
── Column specification ───────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (3): url, host_type, project
dbl (8): ...1, major_releases, duration, author_count, rev_count, status, multi_repo, commits_per_day
lgl (1): commit_freq_above_median
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
N <- nrow (data);
X <- as.matrix(pull(data, multi_repo));
is_censored <- pull(data, status)==0;
times <- pull(data, duration);
msk_censored <- is_censored == 1;
N_censored <- sum(msk_censored);
# put data into a list for Stan
Stan_data <- list (N_uncensored = N - N_censored,
N_censored = N_censored,
numCovariates = ncol(X),
X_censored = as.matrix(X[msk_censored,]),
X_uncensored = as.matrix(X[!msk_censored ,]),
times_censored = times[msk_censored],
times_uncensored = times[!msk_censored])
# fit Stan model
require(rstan)
exp_surv_model_fit <- suppressMessages(stan(model_code = Stan_exponential_survival_model, data = Stan_data))
Warning in system(paste(CXX, ARGS), ignore.stdout = TRUE, ignore.stderr = TRUE) :
error in running command
clang: error: no input files
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000344 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.44 seconds.
Chain 1: Adjust your expectations accordingly!
Chain 1:
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Chain 1:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 2).
Chain 2:
Chain 2: Gradient evaluation took 0.000167 seconds
Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 1.67 seconds.
Chain 2: Adjust your expectations accordingly!
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Chain 2:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000167 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 1.67 seconds.
Chain 3: Adjust your expectations accordingly!
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Chain 3:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.000172 seconds
Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 1.72 seconds.
Chain 4: Adjust your expectations accordingly!
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Chain 4:
# print model fit
print(get_seed(exp_surv_model_fit))
[1] 1781592037
# print fit summary
fit_summary <- summary(exp_surv_model_fit)
print(fit_summary$summary)
mean se_mean sd 2.5% 25% 50%
beta[1] -1.201176 0.0048332048 0.24669382 -1.715388 -1.365972 -1.190598
alpha -4.946324 0.0007286265 0.03972408 -5.024545 -4.973130 -4.946488
times_uncensored_sampled[1] 141.666065 2.3767378381 145.38910208 3.491004 38.549715 95.291852
times_uncensored_sampled[2] 138.878612 2.2296597711 139.56783291 4.474014 39.587905 95.060079
times_uncensored_sampled[3] 144.084841 2.2885804108 146.24543106 3.616957 41.340714 98.868689
times_uncensored_sampled[4] 141.185140 2.2301422457 142.77808281 3.655603 41.098360 98.699825
times_uncensored_sampled[5] 141.286374 2.1645269957 136.98699892 3.473791 42.577496 99.643133
times_uncensored_sampled[6] 139.741502 2.2387923200 142.01027816 3.045270 40.373978 95.083773
times_uncensored_sampled[7] 132.920417 2.1021205882 129.81231582 3.495246 37.728827 93.007772
times_uncensored_sampled[8] 140.060757 2.3153564645 144.68349049 3.326325 37.982147 94.256142
times_uncensored_sampled[9] 140.176585 2.2699092376 142.07812049 3.358885 38.220064 98.859483
times_uncensored_sampled[10] 138.084301 2.1927723385 137.93079440 3.255770 39.475986 96.255466
times_uncensored_sampled[11] 141.357451 2.2456942405 139.98639317 3.247370 39.386826 100.154973
times_uncensored_sampled[12] 140.086411 2.1588488938 137.17803595 4.231262 40.080520 97.799603
times_uncensored_sampled[13] 136.594242 2.2444836051 140.17106767 2.828577 37.670648 93.450522
times_uncensored_sampled[14] 141.875485 2.2989188661 143.97144392 3.828185 40.426656 97.799853
times_uncensored_sampled[15] 140.810964 2.2891163215 141.76372476 3.242956 39.601679 97.949931
times_uncensored_sampled[16] 141.005701 2.2657007521 142.65745586 2.964366 39.347522 95.191537
times_uncensored_sampled[17] 139.784478 2.3238378350 139.43878420 3.449323 40.753544 96.516142
times_uncensored_sampled[18] 141.157066 2.2281256028 143.45266938 2.873292 39.405969 96.164628
times_uncensored_sampled[19] 142.327983 2.2615373620 140.71949831 4.066908 41.155285 97.529493
times_uncensored_sampled[20] 143.131125 2.2325539981 142.31528805 3.719602 42.874640 100.447480
times_uncensored_sampled[21] 140.801308 2.2009512234 139.80536080 3.949775 40.468617 98.952540
times_uncensored_sampled[22] 482.120168 8.0622126693 504.69100419 11.492967 132.884552 323.942419
times_uncensored_sampled[23] 141.114519 2.2779014711 143.67112735 3.043007 40.647998 96.810141
times_uncensored_sampled[24] 144.280766 2.2542619766 142.84646258 2.843033 41.455397 101.172537
times_uncensored_sampled[25] 140.228878 2.2131644007 138.69802510 3.000487 41.855176 99.652053
times_uncensored_sampled[26] 143.097397 2.2745364221 142.82781832 3.470099 41.137559 98.176862
times_uncensored_sampled[27] 139.579791 2.1810112576 140.68725015 4.032686 40.427976 96.618287
times_uncensored_sampled[28] 139.862897 2.3134301693 139.05479099 3.231900 38.963067 100.025420
times_uncensored_sampled[29] 139.457136 2.1180398215 137.28519094 3.455785 39.669927 99.972725
times_uncensored_sampled[30] 142.100915 2.2739159056 142.09046220 4.093291 42.119051 98.314969
times_uncensored_sampled[31] 140.917267 2.1451230511 136.73748898 3.594980 42.349662 102.756844
times_uncensored_sampled[32] 142.040992 2.1795899993 138.14819528 3.625029 42.493164 102.807818
times_uncensored_sampled[33] 142.943524 2.3670119970 144.80793175 3.361040 41.413052 99.587906
times_uncensored_sampled[34] 137.905152 2.1736459377 139.67667770 4.501642 40.017265 95.126271
times_uncensored_sampled[35] 142.417453 2.3270603428 141.04000313 3.768097 41.754004 98.457498
times_uncensored_sampled[36] 143.544963 2.2459534021 144.32366357 3.906894 39.246786 99.501975
times_uncensored_sampled[37] 141.576356 2.2748172890 141.65392449 4.339499 40.202467 98.398429
times_uncensored_sampled[38] 142.120422 2.2652935303 143.32457241 2.909242 41.495026 96.833013
times_uncensored_sampled[39] 144.163058 2.3670145626 145.39540222 3.653107 40.431288 96.401371
times_uncensored_sampled[40] 139.213215 2.2042465077 138.68544692 4.525265 39.587609 97.507297
times_uncensored_sampled[41] 141.147144 2.3003370644 142.48426675 3.252929 41.080354 96.790155
times_uncensored_sampled[42] 139.938426 2.3554226915 145.71951706 3.863699 39.187542 94.689836
times_uncensored_sampled[43] 143.695793 2.3000327323 145.96810741 3.530737 41.044450 99.038842
times_uncensored_sampled[44] 141.308024 2.2382329316 138.71814900 3.869658 42.081540 101.476836
times_uncensored_sampled[45] 142.248264 2.3146859269 146.10204348 3.748352 39.962389 96.941135
times_uncensored_sampled[46] 143.368389 2.2389785271 141.99163310 3.020732 39.908355 98.602428
times_uncensored_sampled[47] 137.470311 2.1974761753 134.13808859 3.860213 41.570876 98.076682
times_uncensored_sampled[48] 140.158646 2.3117331348 142.36381852 3.210394 40.881687 96.966744
times_uncensored_sampled[49] 135.072998 2.2334825767 137.41380715 3.145728 37.548924 92.831917
times_uncensored_sampled[50] 141.907639 2.2768435519 142.25594617 3.479607 39.845276 101.554060
times_uncensored_sampled[51] 145.227746 2.3819285941 147.09770925 4.924185 40.242560 99.837592
times_uncensored_sampled[52] 139.493598 2.3437007357 142.88602492 3.041570 38.893033 95.775486
times_uncensored_sampled[53] 137.305408 2.1301757684 135.81506841 4.093309 40.676282 95.844352
times_uncensored_sampled[54] 144.064204 2.1828581629 140.57859735 4.202244 44.347497 99.919161
times_uncensored_sampled[55] 141.778274 2.2226858077 139.06499823 3.174115 42.696772 100.387588
times_uncensored_sampled[56] 140.950996 2.1835354136 139.31112350 3.834732 38.594049 97.552082
times_uncensored_sampled[57] 141.473647 2.3140071604 139.71177352 3.315157 40.408704 98.414264
times_uncensored_sampled[58] 141.069184 2.2989364060 142.79992139 3.734667 40.881487 96.727333
times_uncensored_sampled[59] 142.571892 2.2264643489 143.92739960 3.002375 40.549000 97.999353
times_uncensored_sampled[60] 141.684232 2.3281006564 142.77653664 3.677932 41.125468 97.945514
times_uncensored_sampled[61] 140.439094 2.2084997290 140.61666058 3.215852 39.731738 97.006842
times_uncensored_sampled[62] 141.855469 2.2828457900 144.48653368 3.715743 41.084327 99.061689
times_uncensored_sampled[63] 141.511545 2.2242155382 139.97120791 3.722338 40.232033 100.117981
times_uncensored_sampled[64] 144.768241 2.3492410881 147.57335054 3.523406 42.112396 99.577577
times_uncensored_sampled[65] 142.113890 2.3049086011 142.84272950 4.113509 41.321736 97.645956
times_uncensored_sampled[66] 142.715661 2.2881652259 143.06021844 4.204077 39.250185 97.529467
times_uncensored_sampled[67] 141.717587 2.2255718832 142.23956081 3.536500 41.382368 98.759014
times_uncensored_sampled[68] 138.622177 2.1286261977 135.83689639 4.286625 39.974760 98.809468
times_uncensored_sampled[69] 138.205831 2.1334740424 136.06999988 3.652522 37.936798 94.049764
times_uncensored_sampled[70] 139.151971 2.0844619834 134.92426439 3.596989 41.030085 99.875286
times_uncensored_sampled[71] 141.716863 2.2751753739 141.23832481 3.429824 40.000302 99.410814
times_uncensored_sampled[72] 140.354219 2.2618460882 140.19847020 3.073971 39.094108 99.934982
times_uncensored_sampled[73] 139.058467 2.1599409915 138.87372685 3.014968 39.155441 95.281408
times_uncensored_sampled[74] 140.264243 2.2468371920 140.88963800 3.254884 39.102908 97.661172
times_uncensored_sampled[75] 142.629355 2.3141526127 146.76969388 3.496939 39.696717 98.389535
times_uncensored_sampled[76] 141.537870 2.3556578143 141.71854389 4.164369 41.036196 97.474912
times_uncensored_sampled[77] 142.789706 2.2345569681 141.61350152 3.320894 41.049970 98.581153
times_uncensored_sampled[78] 141.608554 2.2874088398 145.15862940 3.696131 39.452500 96.741739
times_uncensored_sampled[79] 141.875960 2.3002275957 142.11608378 3.605607 41.345546 98.371112
times_uncensored_sampled[80] 139.954099 2.2339654009 138.80376281 3.411060 41.350382 99.820976
times_uncensored_sampled[81] 141.268911 2.3029753207 143.26361156 3.421019 42.084333 98.818513
times_uncensored_sampled[82] 138.764851 2.1987212521 137.35074391 4.032047 41.166599 96.670695
times_uncensored_sampled[83] 139.617770 2.2551969251 141.90792361 3.228154 39.116694 95.092211
times_uncensored_sampled[84] 140.148668 2.2332272135 140.87727358 3.576160 41.508313 98.389660
times_uncensored_sampled[85] 137.831297 2.1351378297 137.13560017 3.464388 41.893411 94.527528
times_uncensored_sampled[86] 139.983003 2.2657048584 140.94247945 3.841559 39.822481 97.614516
times_uncensored_sampled[87] 144.757120 2.4128285938 148.01969468 3.606300 41.781842 95.458402
times_uncensored_sampled[88] 140.990890 2.1654686932 140.33507450 3.419639 41.493472 97.629832
times_uncensored_sampled[89] 145.921362 2.3170988616 144.24825151 4.169803 43.331303 101.466607
times_uncensored_sampled[90] 140.358493 2.2680828749 140.33900450 3.549338 39.980115 97.431060
times_uncensored_sampled[91] 143.842424 2.2143370906 142.06935542 3.189280 43.072664 102.847611
times_uncensored_sampled[92] 139.873141 2.2306270928 142.23494177 3.584123 39.216249 96.967101
times_uncensored_sampled[93] 139.912440 2.2227518851 137.39576299 3.776574 42.638166 98.835073
times_uncensored_sampled[94] 139.834081 2.1615565760 137.42541861 3.332935 40.457600 97.961057
times_uncensored_sampled[95] 138.724614 2.1638193629 136.51607364 3.675221 41.484836 98.873942
times_uncensored_sampled[96] 142.287076 2.2966128224 143.56158186 3.396738 40.979858 95.996062
times_uncensored_sampled[97] 470.419346 7.9837002566 509.06508801 11.773704 126.328368 311.004290
times_uncensored_sampled[98] 139.959948 2.2722451610 140.96327159 3.139746 39.897990 94.151359
75% 97.5% n_eff Rhat
beta[1] -1.030181 -0.7469734 2605.230 1.0000144
alpha -4.918897 -4.8704006 2972.334 0.9996976
times_uncensored_sampled[1] 194.722847 544.7175407 3741.977 1.0002579
times_uncensored_sampled[2] 191.291427 519.3235876 3918.262 1.0005511
times_uncensored_sampled[3] 196.518672 546.4008510 4083.497 0.9994523
times_uncensored_sampled[4] 193.782093 505.5158551 4098.812 0.9999343
times_uncensored_sampled[5] 198.737365 510.2748018 4005.278 0.9994101
times_uncensored_sampled[6] 193.659666 524.4831589 4023.574 1.0011622
times_uncensored_sampled[7] 185.200021 477.2215211 3813.437 0.9997368
times_uncensored_sampled[8] 190.985478 532.7925869 3904.831 1.0002433
times_uncensored_sampled[9] 195.758946 514.1863959 3917.756 0.9997543
times_uncensored_sampled[10] 194.029842 515.1145130 3956.721 0.9997372
times_uncensored_sampled[11] 198.316982 526.7202731 3885.710 1.0003604
times_uncensored_sampled[12] 195.615158 506.6888176 4037.613 1.0010929
times_uncensored_sampled[13] 187.061154 525.7366072 3900.173 1.0002023
times_uncensored_sampled[14] 196.689893 523.6898827 3921.981 0.9997125
times_uncensored_sampled[15] 195.328129 517.6530579 3835.257 1.0002486
times_uncensored_sampled[16] 198.708711 511.9756111 3964.458 0.9999847
times_uncensored_sampled[17] 193.512859 504.1426564 3600.440 0.9999645
times_uncensored_sampled[18] 197.015490 520.0228254 4145.128 0.9991648
times_uncensored_sampled[19] 196.057955 510.6657387 3871.694 1.0003096
times_uncensored_sampled[20] 197.979830 505.6724242 4063.490 0.9997836
times_uncensored_sampled[21] 194.925870 518.5482170 4034.845 0.9999531
times_uncensored_sampled[22] 653.117113 1832.5337493 3918.706 1.0009409
times_uncensored_sampled[23] 195.932539 525.3382515 3978.040 1.0005423
times_uncensored_sampled[24] 206.422917 518.9943582 4015.413 0.9999585
times_uncensored_sampled[25] 191.176451 517.4587949 3927.473 1.0010869
times_uncensored_sampled[26] 196.909205 531.5529741 3943.118 0.9996271
times_uncensored_sampled[27] 196.117142 504.1686498 4160.961 1.0000618
times_uncensored_sampled[28] 191.155639 506.8186895 3612.926 1.0003351
times_uncensored_sampled[29] 193.835243 486.1928822 4201.256 1.0006226
times_uncensored_sampled[30] 196.530145 522.0865005 3904.641 0.9998308
times_uncensored_sampled[31] 195.855445 506.0342162 4063.224 0.9994377
times_uncensored_sampled[32] 195.348347 518.6885084 4017.361 0.9998363
times_uncensored_sampled[33] 196.061779 532.7993697 3742.689 0.9998279
times_uncensored_sampled[34] 186.714730 511.8631378 4129.241 1.0002533
times_uncensored_sampled[35] 197.699866 521.3385446 3673.409 1.0012065
times_uncensored_sampled[36] 201.121379 521.0573119 4129.273 1.0008278
times_uncensored_sampled[37] 196.673057 530.6569772 3877.610 0.9994468
times_uncensored_sampled[38] 196.449584 531.0603176 4003.062 1.0006229
times_uncensored_sampled[39] 201.168646 530.7775481 3773.110 1.0001917
times_uncensored_sampled[40] 191.603003 513.6095604 3958.599 1.0000605
times_uncensored_sampled[41] 195.022251 523.3560914 3836.638 1.0001536
times_uncensored_sampled[42] 191.916065 540.0462562 3827.346 0.9999510
times_uncensored_sampled[43] 194.389521 538.2976611 4027.615 0.9993602
times_uncensored_sampled[44] 193.025329 508.2093261 3841.103 0.9996265
times_uncensored_sampled[45] 197.899550 519.0226432 3984.084 1.0014658
times_uncensored_sampled[46] 202.185342 519.5880000 4021.848 1.0003423
times_uncensored_sampled[47] 191.189760 492.2800113 3726.112 0.9997242
times_uncensored_sampled[48] 192.512622 533.2412469 3792.485 1.0001976
times_uncensored_sampled[49] 187.050975 498.1236910 3785.259 1.0008131
times_uncensored_sampled[50] 195.915948 517.0783742 3903.682 0.9997927
times_uncensored_sampled[51] 202.373265 536.7053141 3813.769 0.9995429
times_uncensored_sampled[52] 192.580362 518.6366276 3716.851 1.0002914
times_uncensored_sampled[53] 188.827135 508.3487346 4065.042 0.9999416
times_uncensored_sampled[54] 199.653185 521.4928734 4147.509 0.9996281
times_uncensored_sampled[55] 195.554488 520.2221845 3914.529 1.0002554
times_uncensored_sampled[56] 198.275347 507.7371683 4070.531 0.9993803
times_uncensored_sampled[57] 193.800933 518.2160677 3645.328 1.0003335
times_uncensored_sampled[58] 193.533381 519.7307073 3858.354 1.0000805
times_uncensored_sampled[59] 196.349982 523.4866306 4178.837 0.9995865
times_uncensored_sampled[60] 196.962282 519.2426750 3761.059 1.0013303
times_uncensored_sampled[61] 196.483394 511.4932501 4053.954 1.0006242
times_uncensored_sampled[62] 196.395327 517.4923775 4005.914 0.9991557
times_uncensored_sampled[63] 195.235397 529.0680127 3960.260 1.0002929
times_uncensored_sampled[64] 198.921567 546.3886705 3946.033 0.9994881
times_uncensored_sampled[65] 199.112186 516.8469292 3840.687 1.0007362
times_uncensored_sampled[66] 198.025819 507.8301701 3908.976 0.9993072
times_uncensored_sampled[67] 196.958175 519.0116644 4084.675 1.0001665
times_uncensored_sampled[68] 193.757877 512.7611460 4072.271 1.0003412
times_uncensored_sampled[69] 194.418574 495.6979017 4067.711 1.0000171
times_uncensored_sampled[70] 192.382341 498.4917020 4189.789 1.0003175
times_uncensored_sampled[71] 202.383992 509.6913037 3853.677 1.0016848
times_uncensored_sampled[72] 193.283661 509.9856382 3842.027 0.9997392
times_uncensored_sampled[73] 195.591551 507.6503816 4133.866 0.9991428
times_uncensored_sampled[74] 195.678953 532.7622822 3932.013 0.9994165
times_uncensored_sampled[75] 198.505232 528.2722019 4022.433 0.9998455
times_uncensored_sampled[76] 196.214057 513.9600898 3619.336 0.9995988
times_uncensored_sampled[77] 200.688180 528.8843342 4016.303 0.9992569
times_uncensored_sampled[78] 199.416033 513.7748692 4027.153 0.9997417
times_uncensored_sampled[79] 197.204535 520.4447863 3817.199 1.0004171
times_uncensored_sampled[80] 194.422347 502.3808021 3860.554 0.9997646
times_uncensored_sampled[81] 194.907026 525.2005559 3869.842 1.0007590
times_uncensored_sampled[82] 188.825220 514.4649608 3902.309 0.9995800
times_uncensored_sampled[83] 192.427976 527.5321306 3959.536 1.0005054
times_uncensored_sampled[84] 191.326174 531.0945005 3979.386 0.9997225
times_uncensored_sampled[85] 188.804720 517.0816622 4125.234 0.9995875
times_uncensored_sampled[86] 193.799880 510.2772908 3869.699 0.9998329
times_uncensored_sampled[87] 197.789495 560.4066912 3763.449 1.0006651
times_uncensored_sampled[88] 195.813505 519.1462247 4199.800 0.9992951
times_uncensored_sampled[89] 203.617845 532.8294237 3875.538 0.9998936
times_uncensored_sampled[90] 195.637353 531.5125612 3828.591 0.9996407
times_uncensored_sampled[91] 196.858494 535.5516533 4116.360 0.9999694
times_uncensored_sampled[92] 195.613063 517.2956382 4065.918 1.0000902
times_uncensored_sampled[93] 196.123833 490.2550804 3820.892 1.0001418
times_uncensored_sampled[94] 195.710189 498.9309295 4042.043 0.9999087
times_uncensored_sampled[95] 193.190470 496.0872204 3980.390 0.9995826
times_uncensored_sampled[96] 197.244313 529.2732345 3907.517 1.0005322
times_uncensored_sampled[97] 639.688318 1835.0538465 4065.727 1.0009428
times_uncensored_sampled[98] 191.507042 519.3876879 3848.589 0.9996612
[ reached getOption("max.print") -- omitted 547 rows ]
exp_surv_model_draws <- tidybayes::tidy_draws(exp_surv_model_fit)
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
*** recursive gc invocation
exp_surv_model_draws